Diving dinosaurs? Caveats on the use of bone compactness and pFDA for inferring lifestyle.

The lifestyle of spinosaurid dinosaurs has been a topic of lively debate ever since the unveiling of important new skeletal parts for Spinosaurus aegyptiacus in 2014 and 2020. Disparate lifestyles for this taxon have been proposed in the literature; some have argued that it was semiaquatic to varying degrees, hunting fish from the margins of water bodies, or perhaps while wading or swimming on the surface; others suggest that it was a fully aquatic underwater pursuit predator. The various proposals are based on equally disparate lines of evidence. A recent study by Fabbri and coworkers sought to resolve this matter by applying the statistical method of phylogenetic flexible discriminant analysis to femur and rib bone diameters and a bone microanatomy metric called global bone compactness. From their statistical analyses of datasets based on a wide range of extant and extinct taxa, they concluded that two spinosaurid dinosaurs (S. aegyptiacus, Baryonyx walkeri) were fully submerged "subaqueous foragers," whereas a third spinosaurid (Suchomimus tenerensis) remained a terrestrial predator. We performed a thorough reexamination of the datasets, analyses, and methodological assumptions on which those conclusions were based, which reveals substantial problems in each of these areas. In the datasets of exemplar taxa, we found unsupported categorization of taxon lifestyle, inconsistent inclusion and exclusion of taxa, and inappropriate choice of taxa and independent variables. We also explored the effects of uncontrolled sources of variation in estimates of bone compactness that arise from biological factors and measurement error. We found that the ability to draw quantitative conclusions is limited when taxa are represented by single data points with potentially large intrinsic variability. The results of our analysis of the statistical method show that it has low accuracy when applied to these datasets and that the data distributions do not meet fundamental assumptions of the method. These findings not only invalidate the conclusions of the particular analysis of Fabbri et al. but also have important implications for future quantitative uses of bone compactness and discriminant analysis in paleontology.

Thrust production and chordal flexion of the flukes of bottlenose dolphins performing tail stands at different efforts.

Dolphins have become famous for their ability to perform a wide variety of athletic and acrobatic behaviors including high-speed swimming, maneuverability, porpoising and tail stands. Tail stands are a behavior where part of the body is held vertically above the water's surface, achieved through thrust produced by horizontal tail fluke oscillations. Strong, efficient propulsors are needed to generate the force required to support the dolphin's body weight, exhibiting chordwise and spanwise flexibility throughout the stroke cycle. To determine how thrust production, fluke flexibility and tail stroke kinematics vary with effort, six adult bottlenose dolphins (Tursiops truncatus) were tested at three different levels based on the position of the center of mass (COM) relative to the water's surface: low (COM below surface), medium (COM at surface) and high (COM above surface) effort. Additionally, fluke flexibility was measured as a flex index (FI=chord length/camber length) at four points in the stroke cycle: center stroke up (CU), extreme top of stroke (ET), center stroke down (CD) and extreme bottom of stroke (EB). Video recordings were analyzed to determine the weight supported above the water (thrust production), peak-to-peak amplitude, stroke frequency and FI. Force production increased with low, medium and high efforts, respectively. Stroke frequency also increased with increased effort. Amplitude remained constant with a mean 33.8% of body length. Significant differences were seen in the FI during the stroke cycle. Changes in FI and stroke frequency allowed for increased force production with effort, and the peak-to-peak amplitude was higher compared with that for horizontal swimming.

Spin-leap performance by cetaceans is influenced by moment of inertia.

Cetaceans are capable of extraordinary locomotor behaviors in both water and air. Whales and dolphins can execute aerial leaps by swimming rapidly to the water surface to achieve an escape velocity. Previous research on spinner dolphins demonstrated the capability of leaping and completing multiple spins around their longitudinal axis with high angular velocities. This prior research suggested the slender body morphology of spinner dolphins together with the shapes and positions of their appendages allowed for rapid spins in the air. To test whether greater moments of inertia reduced spinning performance, videos and biologging data of cetaceans above and below the water surface were obtained. The principal factors affecting the number of aerial spins a cetacean can execute were moment of inertia and use of control surfaces for subsurface corkscrewing. For spinner dolphin, Pacific striped dolphin, bottlenose dolphin, minke whale and humpback whale, each with swim speeds of 6-7 m s-1, our model predicted that the number of aerial spins executable was 7, 2, 2, 0.76 and 1, respectively, which was consistent with observations. These data implied that the rate of subsurface corkscrewing was limited to 14.0, 6.8, 6.2, 2.2 and 0.75 rad s-1 for spinner dolphins, striped dolphins, bottlenose dolphins, minke whales and humpback whales, respectively. In our study, the moment of inertia of the cetaceans spanned a 21,000-fold range. The greater moments of inertia for the last four species produced large torques on control surfaces that limited subsurface corkscrewing motion and aerial maneuvers compared with spinner dolphins.

Thrust generation and propulsive efficiency in dolphin-like swimming propulsion.

Given growing interest in emulating dolphin morphology and kinematics to design high-performance underwater vehicles, the current research effort is dedicated to studying the hydrodynamics of dolphin-like oscillatory kinematics in forward propulsion. A computational fluid dynamics method is used. A realistic three-dimentional surface model of a dolphin is made with swimming kinematics reconstructed from video recording. The oscillation of the dolphin is found to enhance the attachment of the boundary layer to the posterior body, which then leads to body drag reduction. The flapping motion of the flukes is found to generate high thrust forces in both the downstroke and the upstroke, during which vortex rings are shed to produce strong thrust jets. The downstroke jets are found to be on average stronger than the upstroke jet, which then leads to net positive lift production. The flexion of the peduncle and flukes is found to be a crucial feature of dolphin-like swimming kinematics. Dolphin-inspired swimming kinematics were created by varying the flexion angle of the peduncle and flukes, which then resulted in significant performance variation. The thrust benefits and propulsive efficiency benefits are associated with a slight decrease and slight increase of the flexion of the peduncle and flukes, respectively.

Multiple behaviors for turning performance of Pacific bluefin tuna (Thunnus orientalis).

Tuna are known for exceptional swimming speeds, which are possible because of their thunniform lift-based propulsion, large muscle mass and rigid fusiform body. A rigid body should restrict maneuverability with regard to turn radius and turn rate. To test if turning maneuvers by the Pacific bluefin tuna (Thunnus orientalis) are constrained by rigidity, captive animals were videorecorded overhead as the animals routinely swam around a large circular tank or during feeding bouts. Turning performance was classified into three different types: (1) glide turns, where the tuna uses the caudal fin as a rudder; (2) powered turns, where the animal uses continuous near symmetrical strokes of the caudal fin through the turn; and (3) ratchet turns, where the overall global turn is completed by a series of small local turns by asymmetrical stokes of the caudal fin. Individual points of the rostrum, peduncle and tip of the caudal fin were tracked and analyzed. Frame-by-frame analysis showed that the ratchet turn had the fastest turn rate for all points with a maximum of 302 deg s-1. During the ratchet turn, the rostrum exhibited a minimum global 0.38 body length turn radius. The local turn radii were only 18.6% of the global ratchet turn. The minimum turn radii ranged from 0.4 to 1.7 body lengths. Compared with the performance of other swimmers, the increased flexion of the peduncle and tail and the mechanics of turning behaviors used by tuna overcomes any constraints to turning performance from the rigidity of the anterior body morphology.

Morphological and histochemical characterization of the pectoral fin muscle of batoids.

Batoids differ from other elasmobranch fishes in that they possess dorsoventrally flattened bodies with enlarged muscled pectoral fins. Most batoids also swim using either of two modes of locomotion: undulation or oscillation of the pectoral fins. In other elasmobranchs (e.g., sharks), the main locomotory muscle is located in the axial myotome; in contrast, the main locomotory muscle in batoids is found in the enlarged pectoral fins. The pectoral fin muscles of sharks have a simple structure, confined to the base of the fin; however, little to no data are available on the more complex musculature within the pectoral fins of batoids. Understanding the types of fibers and their arrangement within the pectoral fins may elucidate how batoid fishes are able to utilize such unique swimming modes. In the present study, histochemical methods including succinate dehydrogenase (SDH) and immunofluoresence were used to determine the different fiber types comprising these muscles in three batoid species: Atlantic stingray (Dasyatis sabina), ocellate river stingray (Potamotrygon motoro) and cownose ray (Rhinoptera bonasus). All three species had muscles comprised of two muscle fiber types (slow-red and fast-white). The undulatory species, D. sabina and P. motoro, had a larger proportion of fast-white muscle fibers compared to the oscillatory species, R. bonasus. The muscle fiber sizes were similar between each species, though generally smaller compared to the axial musculature in other elasmobranch fishes. These results suggest that batoid locomotion can be distinguished using muscle fiber type proportions. Undulatory species are more benthic with fast-white fibers allowing them to contract their muscles quickly, as a possible means of escape from potential predators. Oscillatory species are pelagic and are known to migrate long distances with muscles using slow-red fibers to aid in sustained swimming.

Spinosaurus is not an aquatic dinosaur.

A predominantly fish-eating diet was envisioned for the sail-backed theropod dinosaur Spinosaurus aegyptiacus when its elongate jaws with subconical teeth were unearthed a century ago in Egypt. Recent discovery of the high-spined tail of that skeleton, however, led to a bolder conjecture that S. aegyptiacus was the first fully aquatic dinosaur. The 'aquatic hypothesis' posits that S. aegyptiacus was a slow quadruped on land but a capable pursuit predator in coastal waters, powered by an expanded tail. We test these functional claims with skeletal and flesh models of S. aegyptiacus. We assembled a CT-based skeletal reconstruction based on the fossils, to which we added internal air and muscle to create a posable flesh model. That model shows that on land S. aegyptiacus was bipedal and in deep water was an unstable, slow-surface swimmer (<1 m/s) too buoyant to dive. Living reptiles with similar spine-supported sails over trunk and tail are used for display rather than aquatic propulsion, and nearly all extant secondary swimmers have reduced limbs and fleshy tail flukes. New fossils also show that Spinosaurus ranged far inland. Two stages are clarified in the evolution of Spinosaurus, which is best understood as a semiaquatic bipedal ambush piscivore that frequented the margins of coastal and inland waterways.

Fast and Furious: Energetic Tradeoffs and Scaling of High-Speed Foraging in Rorqual Whales.

Although gigantic body size and obligate filter feeding mechanisms have evolved in multiple vertebrate lineages (mammals and fishes), intermittent ram (lunge) filter feeding is unique to a specific family of baleen whales: rorquals. Lunge feeding is a high cost, high benefit feeding mechanism that requires the integration of unsteady locomotion (i.e., accelerations and maneuvers); the impact of scale on the biomechanics and energetics of this foraging mode continues to be the subject of intense study. The goal of our investigation was to use a combination of multi-sensor tags paired with UAS footage to determine the impact of morphometrics such as body size on kinematic lunging parameters such as fluking timing, maximum lunging speed, and deceleration during the engulfment period for a range of species from minke to blue whales. Our results show that, in the case of krill-feeding lunges and regardless of size, animals exhibit a skewed gradient between powered and fully unpowered engulfment, with fluking generally ending at the point of both the maximum lunging speed and mouth opening. In all cases, the small amounts of propulsive thrust generated by the tail were unable to overcome the high drag forces experienced during engulfment. Assuming this thrust to be minimal, we predicted the minimum speed of lunging across scale. To minimize the energetic cost of lunge feeding, hydrodynamic theory predicts slower lunge feeding speeds regardless of body size, with a lower boundary set by the ability of the prey to avoid capture. We used empirical data to test this theory and instead found that maximum foraging speeds remain constant and high (∼4 m s-1) across body size, even as higher speeds result in lower foraging efficiency. Regardless, we found an increasing relationship between body size and this foraging efficiency, estimated as the ratio of energetic gain from prey to energetic cost. This trend held across timescales ranging from a single lunge to a single day and suggests that larger whales are capturing more prey-and more energy-at a lower cost.

Biomechanical energetics of terrestrial locomotion in California sea lions (Zalophus californianus).

Pinnipedia, an order of semi-aquatic marine mammals, adapted a body design that allows for efficient aquatic locomotion but limited terrestrial locomotion. Otariids, like the California sea lion (Zalophus californianus), have enlarged forelimbs and can bring their hindlimbs under the body to locomote quadrupedally on land, but phocids (true seals) have reduced forelimbs and are unable to bring their hindlimbs beneath them during terrestrial locomotion. Because of these differences, phocids are expected to have greater energetic costs when moving on land compared with otariids. The mechanical costs of transport (COT) and power outputs of terrestrial locomotion were first obtained from one male and two female adult California sea lions through video recording locomotion sequences across a level runway. The center of mass, along with six other anatomical points, were digitized to obtain variables such as velocity (V), amplitude of heave (A) and the frequency (f) of oscillations during the locomotion cycle. These variables represent the principal parameters of a biomechanical model that computes the power output of individuals. The three California sea lions in this study averaged a power output of 112.04 W and a COT of 0.63 J kg-1 m-1. This footage was compared against video footage previously recorded of three phocid species (harbor seal, gray seal and northern elephant seal). Power output and mechanical COT were compared for all four pinniped species by tracking the animals' center of mass. The quadrupedal gait of sea lions showed lower vertical displacements of the center of mass, and higher velocities compared with the terrestrial gait of phocids. Northern elephant seals, gray seals and harbor seals showed significantly higher COT and power outputs than the sea lions. California sea lions locomote with lower energetic costs, and thus higher efficiency compared with phocids, proving that they are a mechanically intermediate species on land between terrestrial mammals and phocids. This study provides novel information on the mechanical energy exerted by pinnipeds, particularly California sea lions, to then be used in future research to better understand the limitations of these aquatic mammals.

Slamming dynamics of diving and its implications for diving-related injuries.

In nature, many animals dive into water at high speeds, e.g., humans dive from cliffs, birds plunge, and aquatic animals porpoise and breach. Diving provides opportunities for animals to find prey and escape from predators and is a source of great excitement for humans. However, diving from high platforms can cause severe injuries to a diver. In this study, we demonstrate how similarity in the morphology of diving fronts unifies the slamming force across diving animals and humans. By measuring a time-averaged impulse that increases linearly with the impact height, we are able to estimate the unsteady hydrodynamic forces that an average human body experiences during the slamming phase of a feet-first, hand-first, or head-first dive. We evaluate whether the unsteady forces put the diver at risk of muscle or bone injuries for a particular diving height. Therefore, this study sheds light on a hydrodynamics-based protocol for safe high diving and an evolutionary driver for animal morphology.

Bio-Inspired Propulsion: Towards Understanding the Role of Pectoral Fin Kinematics in Manta-like Swimming.

Through computational fluid dynamics (CFD) simulations of a model manta ray body, the hydrodynamic role of manta-like bioinspired flapping is investigated. The manta ray model motion is reconstructed from synchronized high-resolution videos of manta ray swimming. Rotation angles of the model skeletal joints are altered to scale the pitching and bending, resulting in eight models with different pectoral fin pitching and bending ratios. Simulations are performed using an in-house developed immersed boundary method-based numerical solver. Pectoral fin pitching ratio (PR) is found to have significant implications in the thrust and efficiency of the manta model. This occurs due to more optimal vortex formation and shedding caused by the lower pitching ratio. Leading edge vortexes (LEVs) formed on the bottom of the fin, a characteristic of the higher PR cases, produced parasitic low pressure that hinders thrust force. Lowering the PR reduces the influence of this vortex while another LEV that forms on the top surface of the fin strengthens it. A moderately high bending ratio (BR) can slightly reduce power consumption. Finally, by combining a moderately high BR = 0.83 with PR = 0.67, further performance improvements can be made. This enhanced understanding of manta-inspired propulsive mechanics fills a gap in our understanding of the manta-like mobuliform locomotion. This motivates a new generation of manta-inspired robots that can mimic the high speed and efficiency of their biological counterpart.

Scaling of maneuvering performance in baleen whales: larger whales outperform expectations.

Despite their enormous size, whales make their living as voracious predators. To catch their much smaller, more maneuverable prey, they have developed several unique locomotor strategies that require high energetic input, high mechanical power output and a surprising degree of agility. To better understand how body size affects maneuverability at the largest scale, we used bio-logging data, aerial photogrammetry and a high-throughput approach to quantify the maneuvering performance of seven species of free-swimming baleen whale. We found that as body size increases, absolute maneuvering performance decreases: larger whales use lower accelerations and perform slower pitch-changes, rolls and turns than smaller species. We also found that baleen whales exhibit positive allometry of maneuvering performance: relative to their body size, larger whales use higher accelerations, and perform faster pitch-changes, rolls and certain types of turns than smaller species. However, not all maneuvers were impacted by body size in the same way, and we found that larger whales behaviorally adjust for their decreased agility by using turns that they can perform more effectively. The positive allometry of maneuvering performance suggests that large whales have compensated for their increased body size by evolving more effective control surfaces and by preferentially selecting maneuvers that play to their strengths.

The role of California sea lion (Zalophus californianus) hindflippers as aquatic control surfaces for maneuverability.

California sea lions (Zalophus californianus) are a highly maneuverable species of marine mammal. During uninterrupted, rectilinear swimming, sea lions oscillate their foreflippers to propel themselves forward without aid from the collapsed hindflippers, which are passively trailed. During maneuvers such as turning and leaping (porpoising), the hindflippers are spread into a delta-wing configuration. There is little information defining the role of otarrid hindflippers as aquatic control surfaces. To examine Z. californianus hindflippers during maneuvering, trained sea lions were video recorded underwater through viewing windows performing porpoising behaviors and banking turns. Porpoising by a trained sea lion was compared with sea lions executing the maneuver in the wild. Anatomical points of reference (ankle and hindflipper tip) were digitized from videos to analyze various performance metrics and define the use of the hindflippers. During a porpoising bout, the hindflippers were considered to generate lift when surfacing with a mean angle of attack of 14.6±6.3 deg. However, while performing banked 180 deg turns, the mean angle of attack of the hindflippers was 28.3±7.3 deg, and greater by another 8-12 deg for the maximum 20% of cases. The delta-wing morphology of the hindflippers may be advantageous at high angles of attack to prevent stalling during high-performance maneuvers. Lift generated by the delta-shaped hindflippers, in concert with their position far from the center of gravity, would make these appendages effective aquatic control surfaces for executing rapid turning maneuvers.

Scaling of oscillatory kinematics and Froude efficiency in baleen whales.

High efficiency lunate-tail swimming with high-aspect-ratio lifting surfaces has evolved in many vertebrate lineages, from fish to cetaceans. Baleen whales (Mysticeti) are the largest swimming animals that exhibit this locomotor strategy, and present an ideal study system to examine how morphology and the kinematics of swimming scale to the largest body sizes. We used data from whale-borne inertial sensors coupled with morphometric measurements from aerial drones to calculate the hydrodynamic performance of oscillatory swimming in six baleen whale species ranging in body length from 5 to 25 m (fin whale, Balaenoptera physalus; Bryde's whale, Balaenoptera edeni; sei whale, Balaenoptera borealis; Antarctic minke whale, Balaenoptera bonaerensis; humpback whale, Megaptera novaeangliae; and blue whale, Balaenoptera musculus). We found that mass-specific thrust increased with both swimming speed and body size. Froude efficiency, defined as the ratio of useful power output to the rate of energy input ( Sloop, 1978), generally increased with swimming speed but decreased on average with increasing body size. This finding is contrary to previous results in smaller animals, where Froude efficiency increased with body size. Although our empirically parameterized estimates for swimming baleen whale drag were higher than those of a simple gliding model, oscillatory locomotion at this scale exhibits generally high Froude efficiency as in other adept swimmers. Our results quantify the fine-scale kinematics and estimate the hydrodynamics of routine and energetically expensive swimming modes at the largest scale.

The Role of the Tail or Lack Thereof in the Evolution of Tetrapod Aquatic Propulsion.

Secondary aquatic vertebrates exhibit a diversity of swimming modes that use paired limbs and/or the tail. Various secondarily aquatic tetrapod clades, including amphibians, reptiles, and mammals use transverse undulations or oscillations of the tail for swimming. These movements have often been classified according to a kinematic gradient that was established for fishes but may not be appropriate to describe the swimming motions of tetrapods. To understand the evolution of movements and design of the tail in aquatic tetrapods, we categorize the types of tails used for swimming and examine swimming kinematics and hydrodynamics. From a foundation of a narrow, elongate ancestral tail, the tails used for swimming by aquatic tetrapods are classified as tapered, keeled, paddle, and lunate. Tail undulations are associated with tapered, keeled, and paddle tails for a diversity of taxa. Propulsive undulatory waves move down the tail with increasing amplitude toward the tail tip, while moving posteriorly at a velocity faster than the anterior motion of the body indicating that the tail is used for thrust generation. Aquatic propulsion is associated with the transfer of momentum to the water from the swimming movements of the tail, particularly at the trailing edge. The addition of transverse extensions and flattening of the tail increases the mass of water accelerated posteriorly and affects vorticity shed into the wake for more aquatically adapted animals. Digital Particle Image Velocimetry reveals that the differences were exhibited in the vortex wake between the morphological and kinematic extremes of the alligator with a tapering undulating tail and the dolphin with oscillating wing-like flukes that generate thrust. In addition to exploring the relationship between the shape of undulating tails and the swimming performance across aquatic tetrapods, the role of tail reduction or loss of a tail in aquatic-tetrapod swimming was also explored. For aquatic tetrapods, the reduction would have been due to factors including locomotor and defensive specializations and phylogenetic and physiological constraints. Possession of a thrust-generating tail for swimming, or lack thereof, guided various lineages of secondarily aquatic vertebrates into different evolutionary trajectories for effective aquatic propulsion (i.e., speed, efficiency, and acceleration).

The "dog paddle": Stereotypic swimming gait pattern in different dog breeds.

The term "dog paddle" has been applied to the swimming behavior of various terrestrial and aquatic species. Dog paddling refers to a form of drag-based, paddle propulsion in which the limbs are oriented underneath the body and moved through an arc. Despite the ubiquity of the term, there has been no analysis of the swimming kinematics of dogs. Underwater video was recorded of surface swimming dogs (velocity: 0.4-1.1 m/s) for eight individuals from six breeds, ranging in size from Yorkshire Terrier (3.6 kg) to Newfoundland dog (63.5 kg). The quadrupedal paddling stroke was analyzed to determine kinematics and coordination of the limbs. The paddling stroke represented a modified terrestrial gait, which was outside typical gaits for terrestrial locomotion by dogs. Stroke frequency decreased with increasing body size. The stroke cycle consisted of power and recovery phases. During the power phase, digits of the paw were abducted and the forelimb was swept posteriorly until perpendicular to the body. In the recovery phase, digits were adducted while the brachium was retracted anteriorly and the manus supinated. The power phase was about 34% of stroke cycle and shorter than the recovery phase for both fore and hindlimbs. Maximum velocity during the power phase was greater than the recovery phase. The modified terrestrial gait used for swimming by dogs appears to be stereotypic among breeds, whereas terrestrial locomotion in dogs shows substantial variation in gait. Without constraints imposed by gravity and substrate contact, swimming dogs can utilize a gait profile different from terrestrial gaits. SUMMARY STATEMENT: Despite the ubiquity of the term "dog paddle" to describe the swimming motions of animals, this is the first time that the swimming motions of dogs have been analyzed.

A 60:40 split: Differential mass support in dogs.

Dogs have been bred for different sizes and functions, which can affect their locomotor biomechanics. As quadrupeds, dogs must distribute their mass between fore and hind legs when standing. The mass distribution in dogs was studied to determine if the proportion of supported mass on each limb couplet is dependent on body size. A total of 552 dogs from 123 breeds ranging in size from Chihuahua to Mastiff were examined. Each dog was weighed on a digital scale while standing, alternating foreleg, and hind leg support. The overall "grand" mean proportion of mass on the forelegs to the total mass was 60.4% (range: 47.6-74.4%). The data set indicated no significant change in the ratio with total mass but there was a significant difference by sex. When separated into American Kennel Club categories, no group was notably different from the grand mean or from each other, but when sex was also considered, there was a significant difference that was not specifically discerned by post hoc analysis. The mean for female Hounds was notably below the grand mean. For clades based on genetics, the mean for European origin mastiffs was notably greater than the grand mean and significantly different from UK origin herders and coursers. The mass of the head, chest, and musculature for propulsion could explain the mass support differential. Mass distribution and terrestrial locomotion in dogs shows substantial variation among breeds.

Energetic and physical limitations on the breaching performance of large whales.

The considerable power needed for large whales to leap out of the water may represent the single most expensive burst maneuver found in nature. However, the mechanics and energetic costs associated with the breaching behaviors of large whales remain poorly understood. In this study we deployed whale-borne tags to measure the kinematics of breaching to test the hypothesis that these spectacular aerial displays are metabolically expensive. We found that breaching whales use variable underwater trajectories, and that high-emergence breaches are faster and require more energy than predatory lunges. The most expensive breaches approach the upper limits of vertebrate muscle performance, and the energetic cost of breaching is high enough that repeated breaching events may serve as honest signaling of body condition. Furthermore, the confluence of muscle contractile properties, hydrodynamics, and the high speeds required likely impose an upper limit to the body size and effectiveness of breaching whales.

Three-dimensional scaling laws of cetacean propulsion characterize the hydrodynamic interplay of flukes' shape and kinematics.

Cetaceans convert dorsoventral body oscillations into forward velocity with a complex interplay between their morphological and kinematic features and the fluid environment. However, it is unknown to what extent morpho-kinematic features of cetaceans are intertwined to maximize their efficiency. By interchanging the shape and kinematic variables of five cetacean species, the interplay of their flukes morpho-kinematic features is examined by characterizing their thrust, power and propulsive efficiency. It is determined that the shape and kinematics of the flukes have considerable influence on force production and power consumption. Three-dimensional heaving and pitching scaling laws are developed by considering both added mass and circulatory-based forces, which are shown to closely model the numerical data. Using the scaling relations as a guide, it is determined that the added mass forces are important in predicting the trend between the efficiency and aspect ratio, however, the thrust and power are driven predominately by the circulatory forces. The scaling laws also reveal that there is an optimal dimensionless heave-to-pitch ratio h* that maximizes the efficiency. Moreover, the optimal h* varies with the aspect ratio, the amplitude-to-chord ratio and the Lighthill number. This indicates that the shape and kinematics of propulsors are intertwined, that is, there are specific kinematics that are tailored to the shape of a propulsor in order to maximize its propulsive efficiency.